Spin Crossover of Thiophosgene via Multidimensional Heavy-Atom Quantum Tunneling

Temperature-Dependent Mechanistic Control of Nonadiabatic Tunnelling in Triplet Carbenes

Experiments on three chemically similar triplet carbenes observed the reaction of one at 10 K, another only when heated to 65 K, whereas the third remained stable despite heating. As the products are singlets, it is clear that the reactions involve intersystem crossing in addition to intramolecular hydrogen transfer. Here, instanton theory is used to study various possible reaction mechanisms, including sequential and concerted pathways. The latter describes a new reaction mechanism which involves changing spin state (a nonadiabatic process) while heavy atoms tunnel underneath a barrier (an adiabatic process). In each case, we find that the concerted pathway dominates the rate at low temperatures, but at higher temperatures it switches to a sequential mechanism. The existence of a crossover temperature is the key to explaining the experimental observations and demonstrates that temperature can control the reactivity of triplet carbenes via nonadiabatic tunnelling.

Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem

Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface, whose period is τ = ℏ/(kBT). Unfortunately, the standard theory is only applicable below the "crossover temperature," where the periodic orbit first appears. This paper presents a rigorous semiclassical (ℏ → 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard version of instanton theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e., multi-orbit) terms and provides a framework for further extensions of the theory.

Nonadiabatic Tunneling in Chemical Reactions

Quantum tunneling can have a dramatic effect on chemical reaction rates. In nonadiabatic reactions such as electron transfers or spin crossovers, nuclear tunneling effects can be even stronger than for adiabatic proton transfers. Ring-polymer instanton theory enables molecular simulations of tunneling in full dimensionality and has been shown to be far more reliable than commonly used separable approximations. First-principles instanton calculations predict significant nonadiabatic tunneling of heavy atoms even at room temperature and give excellent agreement with experimental measurements for the intersystem crossing of two nitrenes in cryogenic matrix isolation, the spin-forbidden relaxation of photoexcited thiophosgene in the gas phase, and singlet oxygen deactivation in water at ambient conditions. Finally, an outlook of further theoretical developments is discussed.

A size-consistent multi-state mapping approach to surface hopping

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

Heavy-atom tunnelling in singlet oxygen deactivation predicted by instanton theory with branch-point singularities

The reactive singlet state of oxygen (O2) can decay to the triplet ground state nonradiatively in the presence of a solvent. There is a controversy about whether tunnelling is involved in this nonadiabatic spin-crossover process. Semiclassical instanton theory provides a reliable and practical computational method for elucidating the reaction mechanism and can account for nuclear quantum effects such as zero-point energy and multidimensional tunnelling. However, the previously developed instanton theory is not directly applicable to this system because of a branch-point singularity which appears in the flux correlation function. Here we derive a new instanton theory for cases dominated by the singularity, leading to a new picture of tunnelling in nonadiabatic processes. Together with multireference electronic-structure theory, this provides a rigorous framework based on first principles that we apply to calculate the decay rate of singlet oxygen in water. The results indicate a new reaction mechanism that is 27 orders of magnitude faster at room temperature than the classical process through the minimum-energy crossing point. We find significant heavy-atom tunnelling contributions as well as a large temperature-dependent H2O/D2O kinetic isotope effect of approximately 20, in excellent agreement with experiment.

Classically forbidden nonadiabatic transitions in multidimensional chemical dynamics

An accurate method is proposed to deal with such nonadiabatic transitions as those energetically inaccessible, namely, classically forbidden transitions. This is formulated by using the corresponding Zhu-Nakamura formulas and finding the optimal paths in the classically forbidden tunneling regions that maximize the overall transition probabilities. This can be done for both the nonadiabatic tunneling type (so-called normal case in electron transfer) in which two diabatic potentials have opposite signs of slopes and the Landau-Zener type (inverted case) in which two diabatic potentials have the same sign of slopes. The method is numerically demonstrated to be useful for clarifying chemical and biological dynamics.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

Quantum and anharmonic effects in non-adiabatic transition state theory

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. In this paper, the interplay between quantum effects-for motion across or along the seam of crossing-and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N2O ↔ N2 + O(3P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3A'-1A' seam of N2O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ∼20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N-N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (∼250 K for N2O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions-harmonic behavior, classical motion, linear terms, and weak coupling-should be verified on a case-by-case basis.

Competing quantum effects in heavy-atom tunnelling through conical intersections

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

Transition metal oxide complexes as molecular catalysts for selective methane to methanol transformation: any prospects or time to retire?

Transition metal oxides have been extensively used in the literature for the conversion of methane to methanol. Despite the progress made over the past decades, no method with satisfactory performance or economic viability has been detected. The main bottleneck is that the produced methanol oxidizes further due to its weaker C-H bond than that of methane. Every improvement in the efficiency of a catalyst to activate methane leads to reduction of the selectivity towards methanol. Is it therefore prudent to keep studying (both theoretically and experimentally) metal oxides as catalysts for the quantitative conversion of methane to methanol? This perspective focuses on molecular metal oxide complexes and suggests strategies to bypass the current bottlenecks with higher weight on the computational chemistry side. We first discuss the electronic structure of metal oxides, followed by assessing the role of the ligands in the reactivity of the catalysts. For better selectivity, we propose that metal oxide anionic complexes should be explored further, while hydrophylic cavities in the vicinity of the metal oxide can perturb the transition-state structure for methanol increasing appreciably the activation barrier for methanol. We also emphasize that computational studies should target the activation reaction of methanol (and not only methane), the study of complete catalytic cycles (including the recombination and oxidation steps), and the use of molecular oxygen as an oxidant. The titled chemical conversion is an excellent challenge for theory and we believe that computational studies should lead the field in the future. It is finally shown that bottom-up approaches offer a systematic way for exploration of the chemical space and should still be applied in parallel with the recently popular machine learning techniques. To answer the question of the title, we believe that metal oxides should still be considered provided that we change our focus and perform more systematic investigations on the activation of methanol.

Quantum Tunneling in Reactions Modulated by External Electric Fields: Reactivity and Selectivity

Quantum tunneling and external electric fields (EEFs) can promote some reactions. However, the synergetic effect of an EEF on a tunneling-involving reaction and its temperature-dependence is not very clear. In this study, we extensively investigated how EEFs affect three reactions that involve hydrogen- or (ground- and excited-state) carbon-tunneling using reliable DFT, DLPNO-CCSD(T1), and variational transition-state theory methods. Our study revealed that oriented EEFs can significantly reduce the barrier and corresponding barrier width (and vice versa) through more electrostatic stabilization in transition states. These EEF effects enhance the nontunneling and tunneling-involving rates. Such EEF effects also decrease the crossover temperatures and quantum tunneling contribution, albeit with lower and thinner barriers. Moreover, EEFs can modulate and switch on/off the tunneling-driven 1,2-H migration of hydroxycarbenes under cryogenic conditions. Furthermore, our study predicts for the first time that EEF/tunneling synergy can control the chemo- or site-selectivity of one molecule bearing two similar/same reactive sites.

Simultaneous Tunneling Control in Conformer-Specific Reactions

We present here a new example of chemical reactivity governed by quantum tunneling, which also highlights the limitations of the classical theories. The syn and anti conformers of a triplet 2-formylphenylnitrene, generated in a nitrogen matrix, were found to spontaneously rearrange to the corresponding 2,1-benzisoxazole and imino-ketene, respectively. The kinetics of both transformations were measured at 10 and 20 K and found to be temperature-independent, providing clear evidence of concomitant tunneling reactions (heavy-atom and H-atom). Computations confirm the existence of these tunneling reaction pathways. Although the energy barrier between the nitrene conformers is lower than any of the observed reactions, no conformational interconversion was observed. These results demonstrate an unprecedented case of simultaneous tunneling control in conformer-specific reactions of the same chemical species. The product outcome is impossible to be rationalized by the conventional kinetic or thermodynamic control.

Heavy-Atom Quantum Tunnelling in Spin Crossovers of Nitrenes

We simulate two recent matrix-isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak-coupling method (based on a linear approximation of the potentials) in describing these deep-tunnelling reactions. The more rigorous approach of semiclassical golden-rule instanton theory in conjunction with double-hybrid density-functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy-atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Improved microcanonical instanton theory

Canonical (thermal) instanton theory is now routinely applicable to complex gas-phase reactions and allows for the accurate description of tunnelling in highly non-separable systems. Microcanonical instanton theory is by contrast far less well established. Here, we demonstrate that the best established microcanonical theory [S. Chapman, B. C. Garrett and W. H. Miller, J. Chem. Phys., 1975, 63, 2710-2716], fails to accurately describe the deep-tunnelling regime for systems where the frequencies of the orthogonal modes change rapidly along the instanton path. By taking a first principles approach to the derivation of microcanonical instanton theory, we obtain an improved method, which accurately recovers the thermal instanton rate when integrated over energy. The resulting theory also correctly recovers the separable limit and can be thought of as an instanton generalisation of Rice-Ramsperger-Kassel-Marcus (RRKM) theory. When combined with the density-of-states approach [W. Fang, P. Winter and J. O. Richardson, J. Chem. Theory Comput., 2021, 17, 40-55], this new method can be straightforwardly applied to real molecular systems.

Nonadiabatic instanton rate theory beyond the golden-rule limit

Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ →0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.